Generalized Bose-Fermi statistics and structural correlations in weighted networks

TL;DR

This paper introduces a generalized statistical framework unifying Bose and Fermi statistics to analyze weighted networks, revealing stronger-than-expected correlations and challenging previous assumptions about their null models.

Contribution

It develops a new class of generalized statistics applicable to weighted networks, providing insights into their structural correlations and topological biases.

Findings

Weighted networks exhibit stronger correlations than previously thought.

Null models for weighted networks need systematic redefinition.

The new statistics unify Bose and Fermi behaviors in network analysis.

Abstract

We derive a class of generalized statistics, unifying the Bose and Fermi ones, that describe any system where the first-occupation energies or probabilities are different from subsequent ones, as in presence of thresholds, saturation, or aging. The statistics completely describe the structural correlations of weighted networks, which turn out to be stronger than expected and to determine significant topological biases. Our results show that the null behavior of weighted networks is different from what previously believed, and that a systematic redefinition of weighted properties is necessary.